Double pants decompositions were introduced by the authors in 2011, together with a flip-twist groupoid acting on these decompositions. It was shown that flip-twist groupoid acts transitively on a certain topological class of the decompositions, however, recently Randich discovered a serious mistake in the proof. In this note we present a new proof of the result, accessible without reading the initial paper.
Felikson, A., & Natanzon, S. (2017). Double Pants Decompositions Revisited. Moscow mathematical journal, 17(1), 51-58